The temperaments listed are 72edo-distinct, meaning that they are all different even if tuned in 72edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
72 23	<<30 1 -68]]		15.274	931322574615478515625/885443715538058477568
36 13	<<12 -2 -31]]		6.558	2197265625/2147483648
24 1	<<18 3 -37]]		8.789	3814697265625/3710851743744
18 5	<<48 4 -105]]		24.043	{{-105 -4 48>>
72 19	<<6 5 -6]]	Hanson	2.685	15625/15552
12 1	<<108 6 -241]]		54.584	{{-241 -6 108>>
72 7	<<6 -7 -25]]	Ampersand	4.815	34171875/33554432
9 4	<<24 8 -43]]		11.22	59604644775390625/57711166318706688
8 1	<<18 -9 -56]]		11.188	75084686279296875/72057594037927936
36 17	<<60 62 -41]]		27.509	{{-41 -62 60>>
72 11	<<30 -11 -87]]		17.697	{{-87 11 30>>
6 1	<<0 12 19]]	Compton	4.218	531441/524288
72 35	<<30 13 -49]]		13.746	931322574615478515625/897524058588526411776
36 7	<<60 14 -117]]		28.753	{{-117 -14 60>>
24 5	<<54 57 -35]]		24.859	{{-35 -57 54>>
9 2	<<24 -16 -81]]		15.929	2565784513950347900390625/2417851639229258349412352
72 31	<<6 17 13]]	Gravity	5.177	129140163/128000000
4 1	<<36 18 -55]]		16.323	14551915228366851806640625/13958294159168762755940352
72 5	<<6 -19 -44]]		8.646	18160335421875/17592186044416
18 1	<<48 52 -29]]		22.217	{{-29 -52 48>>
24 7	<<54 21 -92]]		24.95	{{-92 -21 54>>
36 11	<<12 22 7]]	Unidec	7.088	31381059609/31250000000
72 1	<<30 49 8]]		16.415	239299329230617529590083/238418579101562500000000
3 1	<<72 -24 -205]]		41.926	{{-205 24 72>>
72 25	<<42 47 -23]]		19.587	{{-23 -47 42>>
36 1	<<12 -26 -69]]		13.345	620572711994384765625/590295810358705651712
8 3	<<18 27 1]]	Ennealimmal	9.386	7629394531250/7625597484987
18 7	<<48 28 -67]]		21.556	{{-67 -28 48>>
72 29	<<6 29 32]]		9.054	68630377364883/67108864000000
12 5	<<36 42 -17]]		16.975	14551915228366851806640625/14341765743445587946242048
72 17	<<6 -31 -63]]		12.723	9651146816936671875/9223372036854775808
9 1	<<24 32 -5]]		11.847	59604644775390625/59296646043258912
24 11	<<18 39 20]]		12.119	4052555153018976267/400
36 5	<<60 38 -79]]		26.843	{{-79 -38 60>>
72 13	<<30 37 -11]]		14.389	931322574615478515625/922181439264762599424
2 1	<<144 36 -277]]		68.703	{{-277 -36 144>>

7-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
72 23	<<30 1 -10 -68 -100 -26]]		14.338	1029/1024 9765625/9633792
36 13	<<12 -2 20 -31 -2 52]]	Wizard	6.372	225/224 118098/117649
24 1	<<18 3 42 -37 16 89]]		10.447	225/224 516560652/514714375
18 5	<<24 -4 -32 -62 -118 -63]]		15.506	33075/32768 390625/388962
72 29	<<6 5 22 -6 18 37]]	Catakleismic	4.684	225/224 4375/4374
12 1	<<36 6 12 -74 -82 11]]		14.649	2401/2400 9765625/9633792
72 17	<<6 -7 -2 -25 -20 15]]	Miracle	3.991	225/224 1029/1024
9 4	<<24 8 -8 -43 -80 -41]]		11.17	1029/1024 390625/387072
8 1	<<18 -9 18 -56 -22 67]]		9.546	225/224 40353607/40310784
36 7	<<12 10 -28 -12 -78 -93]]		10.777	15625/15552 33075/32768
72 35	<<30 61 38 27 -24 -83]]		15.688	2401/2400 43046721/42875000
6 1	<<0 12 24 19 38 22]]	Waage	5.927	225/224 250047/250000
72 11	<<30 13 14 -49 -62 -4]]		11.448	2401/2400 390625/387072
36 17	<<12 58 68 64 74 -5]]		17.548	321489/320000 3796875/3764768
24 5	<<18 15 -6 -18 -60 -56]]	Tritikleismic	8.707	1029/1024 15625/15552
9 1	<<24 -16 16 -81 -42 82]]		13.172	225/224 13841287201/13759414272
72 31	<<6 17 46 13 56 59]]	Marvo	9.910	225/224 78125000/78121827
4 1	<<36 18 36 -55 -44 33]]		13.461	16875/16807 390625/387072
72 5	<<6 -19 -26 -44 -58 -7]]		8.954	225/224 156250000/155649627
18 7	<<24 20 16 -24 -42 -19]]	Quadritikleismic	8.908	2401/2400 15625/15552
24 7	<<18 51 66 39 54 10]]		15.417	177147/175616 250047/250000
36 1	<<12 22 -4 7 -40 -71]]	Unidec	7.662	1029/1024 4375/4374
72 25	<<30 49 14 8 -62 -105]]		14.645	4375/4374 823543/819200
3 1	<<0 24 -24 38 -38 -123]]		10.92	19683/19600 33075/32768
72 1	<<30 25 38 -30 -24 18]]		11.259	15625/15552 16875/16807
36 11	<<12 46 44 45 36 -27]]		12.434	16875/16807 177147/175616
8 3	<<18 27 18 1 -22 -34]]	Ennealimmal	7.714	2401/2400 4375/4374
18 1	<<24 44 64 14 34 25]]		14.117	19683/19600 390625/388962
72 19	<<6 29 -2 32 -20 -86]]	Hemiseven	8.570	1029/1024 19683/19600
12 5	<<36 30 60 -36 -6 55]]		14.767	15625/15552 118098/117649
72 7	<<6 41 22 51 18 -64]]		10.742	2401/2400 177147/175616
9 2	<<24 32 40 -5 -4 3]]	Octoid	10.207	4375/4374 16875/16807
24 11	<<18 39 42 20 16 -12]]	Mirkat	10.652	16875/16807 19683/19600
36 5	<<12 34 20 26 -2 -49]]	Harry	8.457	2401/2400 19683/19600
72 13	<<30 37 62 -11 14 40]]		13.883	4375/4374 3796875/3764768
2 1	<<0 36 0 57 0 -101]]		10.957	1029/1024 118098/117649

11-limit temperaments

Period generator	Wedgie	Name	Complexity	Commas
72 23	<<30 1 -10 39 -68 -100 -42 -26 87 144]]		13.253	385/384 441/440 1171875/1162084
36 13	<<12 -2 20 -6 -31 -2 -51 52 -7 -86]]	Wizard	6.421	225/224 385/384 4000/3993
24 1	<<18 3 42 45 -37 16 9 89 94 -19]]		9.837	225/224 243/242 12005/11979
18 5	<<24 -4 40 60 -62 -4 12 104 153 30]]		12.855	225/224 243/242 117649/117128
72 29	<<6 5 22 -21 -6 18 -54 37 -66 -135]]	Catakleismic	7.254	225/224 385/384 4375/4374
12 1	<<36 6 12 18 -74 -82 -96 11 21 9]]		12.763	385/384 1375/1372 9375/9317
72 17	<<6 -7 -2 15 -25 -20 3 15 59 49]]	Miracle	4.405	225/224 385/384 441/440
9 4	<<24 8 -8 24 -43 -80 -45 -41 28 95]]		9.859	385/384 441/440 9375/9317
8 1	<<18 -9 18 9 -56 -22 -48 67 52 -37]]	Enneaportent	8.286	225/224 385/384 12005/11979
36 7	<<12 10 44 30 -12 36 6 74 35 -68]]	Bikleismic	8.191	225/224 243/242 4375/4356
72 35	<<30 -11 38 3 -87 -24 -99 119 45 -123]]		14.155	225/224 385/384 5359375/5314683
6 1	<<0 12 24 36 19 38 57 22 42 18]]	Compton	6.767	225/224 441/440 4375/4356
72 11	<<30 13 14 3 -49 -62 -99 -4 -38 -40]]		10.735	385/384 1375/1372 4000/3993
36 17	<<12 -14 -4 -42 -50 -40 -108 30 -49 -104]]		10.342	225/224 1029/1024 4375/4356
24 5	<<18 15 -6 9 -18 -60 -48 -56 -31 46]]	Tritikleismic	7.587	385/384 441/440 4000/3993
9 1	<<24 -16 16 24 -81 -42 -45 82 111 12]]		11.615	225/224 385/384 324135/322102
72 31	<<6 17 46 15 13 56 3 59 -24 -117]]	Marvo	8.731	225/224 243/242 4000/3993
4 1	<<36 18 36 54 -55 -44 -39 33 63 27]]		12.044	540/539 1375/1372 15625/15488
72 5	<<6 -19 -26 -21 -44 -58 -54 -7 17 31]]	Marvolo	7.935	225/224 441/440 4000/3993
18 7	<<24 20 16 60 -24 -42 12 -19 70 113]]		9.965	243/242 441/440 15625/15488
24 7	<<18 -21 -6 -27 -75 -60 -105 45 10 -55]]		11.495	225/224 1029/1024 4000/3993
36 1	<<12 22 -4 -6 7 -40 -51 -71 -90 -3]]	Unidec	7.532	385/384 441/440 12005/11979
72 25	<<30 49 14 39 8 -62 -42 -105 -79 61]]		12.684	441/440 4000/3993 41503/41472
3 1	<<0 24 -24 0 38 -38 0 -123 -83 83]]	Hours	9.462	243/242 385/384 9801/9800
72 1	<<30 25 38 39 -30 -24 -42 18 4 -22]]	Sqrtphi	9.756	540/539 1375/1372 4375/4356
36 11	<<12 -26 -28 -6 -69 -78 -51 8 76 80]]		10.906	225/224 441/440 102487/102400
8 3	<<18 27 18 45 1 -22 9 -34 11 64]]	Ennealimnic	7.578	243/242 441/440 4375/4356
18 1	<<24 44 64 60 14 34 12 25 -13 -53]]		12.384	243/242 1375/1372 6250/6237
72 19	<<6 29 -2 -21 32 -20 -54 -86 -149 -52]]	Hemiseven	9.733	385/384 441/440 19683/19600
12 5	<<36 42 12 54 -17 -82 -39 -90 -20 110]]		13.571	441/440 4375/4356 41503/41472
72 7	<<6 41 22 15 51 18 3 -64 -107 -34]]	Neominor	9.493	243/242 441/440 35937/35840
9 2	<<24 32 40 24 -5 -4 -45 3 -55 -71]]	Octoid	9.170	540/539 1375/1372 4000/3993
24 11	<<18 39 42 9 20 16 -48 -12 -114 -120]]	Mirkat	10.575	540/539 1375/1372 8019/8000
36 5	<<12 34 20 30 26 -2 6 -49 -48 15]]	Harry	7.373	243/242 441/440 4000/3993
72 13	<<30 37 -10 3 -11 -100 -99 -127 -121 43]]		14.463	385/384 441/440 1953125/1948617
2 1	<<0 36 0 36 57 0 57 -101 -41 101]]		10.349	540/539 1029/1024 4000/3993